A new calculation of potential energy of supporting springs and the application in design of vibrating ring gyroscope

High-performance micro-gyroscopes are needed in many applications, including inertial navigation, control, and defense/avionics/space. The ring gyroscope provides a number of advantages, including excellent mode matching, high-resolution; low zero-rate output, and long-term stability. In order to get more accurate drive/control/sense policy and to improve the performance of vibrating ring gyroscope (VRG), potential energy of the semi-circular cantilever supporting spring in VRG is expressed as the function of general coordinates; By calculating the partial differentials of the potential energy the disturbing items, actual stiffness, coupling stiffness of VRG are obtained; Resonant frequency and frequency splitting of the sensing modes of VRG are obtained from the actual stiffness and coupling stiffness. The method presented in this paper is suitable to get the above key parameters of the VRG both with ideal symmetrical structure and structure of fabrication errors. Complex mechanical and material principles are avoided and the compact analytical calculation is presented in detail in this paper. The conclusions and simulations in this paper will be used in developing the drive/control/sensing policy of high-performance VRG lately.